There are numerous achievements about completing special events (which are small side quests you can do without impeding on your current quest progress). Also, most if not all include some kind of XP/Gold reward for completion.
I tried clicking on the achievements, but as far as I can tell, there's no indication of what zone the event actually occurs in, and I don't want to re-play entire quests just to get an event if I don't have to.
Quests marked with a + have associated event achievements.
+Carrion Farm - Forsaken Grounds in Fields of Misery (It's a big obvious farm with lots of Plague Carriers and 4 Plague Nests that can randomly spawn in several locations across FoM, but I often find it to the middle northern section of the map. There, you will encounter a Beleaguered Farmer with a quest marker)
The Family of Rathe - Decaying Crypt Level 2 in Fields of Misery (In the random dungeon, Decaying Crypt, you will encounter the ghost, Willa Rathe with a quest marker standing in a body of water)
The Precious Ores - The Lost Mine Level 2 in Fields of Misery (In the random dungeon The Lost Mine, you will encounter Tashun the Miner with a quest marker)
+The Matriarch's Bones - a randomly generated crypt in Cemetery of the Forsaken (In the crypt, you'll see urns glowing blue and the ghost, Lady Dunhyld with a quest marker)
+Jar of Souls - a randomly generated crypt in Cemetery of the Forsaken (In the center of the crypt is a gated room with a blue jar accessible from 4 sides. The blue jar starts the event)
+The Last Stand of the Ancients - The Festering Woods (It's a grave marker on the top of a hill. I always see it shortly after entering Festering Woods. The path splits at the start and once you pass the split, it's in the middle of the map.)
+Eternal War - The Festering Woods (It's a square stone on the ground called the Nephalem Monument that is randomly found in the middle part of The Festering Woods).
The Sacrificial Hermit - Wortham Bluffs during the quest Trailing the Coven (After crossing the bridge right before The Caverns of Aranae, you wili randomly encounter Rodger the Alchemist and the event will begin)
+Revenge of Gharbad - Southern Highlands (A randomly occurring event in the random location Ancient Pyre that appears in the north-east part of the map, to the right of the road just south-east of the goatmen camp, you will encounter the ghost Gharbad with a quest marker.)
The Scavenged Scabbard - The Watch Tower Level 2 in Southern Highlands (In the random location The Watch Tower, you will rarely encounter Vendel the Armorsmith and the event will begin)(This is where you get the book Scabbard of Talic the Defender associated with the general Act I people lore achievement, A Quick Study)
A Stranger in Need - Halls of Agony Level 2 (In the fiery pit just beside the exit to Halls of Agony Level 2, there will randomly be an iron maiden right in the north corner. Approach the pit to hear Merhan call for help and begin the event.) (This is where you get the book A Prisoner's Journal associated with the general Act I people lore achievement, A Quick Study)
Reputation Restored - Highlands Passage (Just outside of Halls of Agony Level 2, you will randomly encounter Kyr the Weaponsmith and the event will begin)
+A Miner's Gold - Howling Plateau (You randomly encounter an NPC with a quest marker near a crane with a resplendent chest atop a hill on a randomly appearing event location in the north-central part of the Howling plateau, just south of the bridge to Black Canyon Mines.)
+Lair of the Lacuni - Abandoned Mineworks in the Howling Plateau (You begin this quest upon entering the random dungeon Abandoned Mineworks.)
+Guardian Spirits - Stinging Winds (In a random event location in Stinging Winds, you may randomly find a Dying Necromancer with a quest marker atop a rocky outcropping with a building on it. If the NPC isn't there, there's a chest in stead).
+The Restless Sands - Stinging Winds (In a random event location, you encounter Mehtan the Necromancer with a quest marker.)
+Crumbling Vault - The Crumbling Vault and Vault Treasure Room in Stinging Winds (Complete the timed random dungeon and reach the Vault Treasure Room)
+The Rygnar Idol - Chamber of the Lost Idol in Stinging Winds (Once you enter the chamber, you will meet Poltahr with a quest marker)
+Prisoners of Kamyr - Dahlgur Oasis (in a random location in the Dahlgur Oasis, you encounter guards tied to posts. By untying any of them, you begin the event.)
+Shrine of Rakanishu - Dahlgur Oasis (in the random location that appears in the south-east part of the map where a bunch of enemies performing a ceremony atop a hill can be seen, you can begin this quest by climbing the hill. Keep the sword you get as it is used for the Bashanishu achievement)
+Lost Treasure of Khan Dakab - Tomb of Khan Dakab in Dahlgur Oasis (Enter the random dungeon Tomb of Khan Dakab to begin the event.)
Sardar's Treasure - Tomb of Sardar in Dahlgur Oasis (Enter the random dungoeon Tomb of Sardar to begin the event.)
+Waiting for Reinforcements - Stonefort during the quest Turning the Tide (Shortly after entering Stonefort as part of the quest Turning the Tide, you will encounter Captain Haile with a quest marker)
Raising Recruits - Stonefort during the quest Turning the Tide (At the first catapault as part of the quest Turning the Tide, you will encounter Sergeant Burroughs with a quest marker)(this together with Protect and Serve have an achievement for not letting anyone die)
Protect and Serve - Stonefort during the quest Turning the Tide (At the second catapault as part of the quest Turning the Tide, you will encounter Lieutenant Lavail with a quest marker)(this together with Raising Recruits have an achievement for not letting anyone die)
Manual Overide - Stonefort during the quest Turning the Tide (At the third catapault as part of the quest Turning the Tide, you will encounter Lieutenant Clyfton with a quest marker)
+Forged in Battle - The Keep Depths Level 1 (Somewhere with a lava pit and a forge in The Keep Depths Level 1, you may randomly encounter Ironsmith Maldonado with a quest marker)
+Blood Ties - The Barracks Level 2 (You will randomly encounter a Guard of the Keep with a quest marker near the entrance to The Barracks Level 2)
+Tide of Battle - The Battlefield (You will randomly encounter Colonel Severyn with quest marker on The Battlefields. Sometimes, the quest begins as soon as you approach)
+Triage - The Battlefields (You will randomly meet Sergeant Brooks with a quest marker on The Battlefields)
+Blaze of Glory - Rakkis Crossing(You will randomly meet Captain Haile with a quest marker by a flaming crack in the middle of the bridge on the raised section for the first part of Rakkis Crossing)
+Crazy Climber - Rakkis Crossing (You will randomly encounter the injured Private James with a quest marker by a set of stairs on the north side of the bridge on the raised section for the first part of Rakkis Crossing)